Sarkhosh Seddighi Chaharborj

Study of Quadrupole Mass Filter Supplied with a New Impulsional Potential

The paper reports on some theoretical studies concerning the impulsional mode of a quadrupole mass filter (QMF) supplied with a new periodic impulsional radio frequency voltage of the form Vaccos(ωt)⌊1 + kcos(⅓ωt)⌋/1 – √kcos(2ωt) with 0 ≤ k < 1 (⌊.⌋ means floor function) and eventually compares it to the classical sinusoidal case, k = 0. The physical properties of the confined ions in the r and z directions are illustrated and the fractional mass resolutions m/Δm of the confined ions in the first stability regions of both potential were analyzed for hydrogen isotopes and presented.

On the Asymptotical and Practical Stability of Stochastic Control Systems

The asymptotical and practical stability in probability of stochastic control systems by means of feedback laws is provided. The main results of this work enable us to derive the sufficient conditions for the existence of control Lyapunov function that play a leading role in the existence of stabilizing feedback laws. Particularly, the sufficient conditions for practical stability in probability are established and numerical examples are also given to illustrate the usefulness of our results.

An Iterative Method for Solving Fuzzy Fractional Differential Equations

The aim of this paper is to solve fuzzy fractional differential equations (FFDEs) of the Caputo type. The basic idea is to convert FFDEs to a type of fuzzy Volterra integral equation. Then the obtained Volterra integral equation will be exploited with some suitable quadrature rules to get a fractional predictor-corrector method. The results show that the proposed method exhibit high precision with low cost.

Optimum Radius Size between Cylindrical Ion Trap and Quadrupole Ion Trap

Quadrupole ion trap mass analyzer with a simplified geometry, namely, the cylindrical ion trap (CIT), has been shown to be well-suited using in miniature mass spectrometry and even in mass spectrometer arrays. Computation of stability regions is of particular importance in designing and assembling an ion trap. However, solving CIT equations are rather more dif- ficult and complex than QIT equations, so, analytical and matrix methods have been widely used to calculate the stability regions. In this article we present the results of numerical simulations of the physical properties and the fractional mass resolu- tions of the confined ions in the first stability region was analyzed by the fifth order Runge-Kutta method (RKM5) at the optimum radius size for both ion traps. Because of similarity the both results, having determining the optimum radius, we can make much easier to design CIT. Also, the simulated results has been performed a high precision in the resolution of trapped ions at the optimum radius size.

A notion of stability in probability of stochastic nonlinear systems

The concepts of stability in probability of nontrivial solutions for stochastic nonlinear systems are analyzed in terms of a control Lyapunov function which is smooth except possibly at the origin. We show under certain hypothesis that the neighborhood of the origin is stable in probability. An illustrating example is provided.MSC:60H10, 93C10, 93D05, 93D15, 93D21, 93E15.

Exponential input-to-state stability of composite stochastic systems

Sufficient conditions for the exponential input-to-state stability in probability in r th mean and for the almost sure exponential input-to-state stability in probability of a composite stochastic system are established. Illustrating example is provided to validate our results.MSC:60H10, 93C10, 93D05, 93D15, 93D21, 93E15.

Mass Resolution Study in the Cylindrical Ion Trap by Using Three-Point One Block Method

Motion equations in cylindrical ion trap (CIT) coupled in u and v (respective r and z), and thus, can only be treated as a rough approximation. Hence, studies on cylindrical ion trap (CIT) equations are more complicated and involved. Therefore, a three point one block method (3POBM) of Adams Moulton type is presented to study a cylindrical ion trap (CIT) motion equations. The advantage of the three point one block method (3POBM) is to estimate the approximate solutions directly at three points simultaneously. Numerical results from three point one block method (3POBM) will compare with fifth order Runge-Kutta method (RKM5). The proposed three points one block method has a potential application to solve complicated linear and nonlinear equations of the charge particle confinement in the cylindrical field especially in fine tuning accelerators, and generally speaking, in physics of high energy. The physical properties of the confined ions in the r and z axises are illustrated and the fractional mass resolutions m/Δm of the confined ions in the first stability region was analyzed by the fifth order Runge-Kutta method (RKM5) and three points one block method (3POBM).

Applications of Stochastic Process in the Quadrupole Ion traps

The Brownian motion or Wiener process, as the physical model of the stochastic procedure, is observed as an indexed collection random variables. Stochastic procedure are quite influential on the confinement potential fluctuation in the quadrupole ion trap (QIT). Such effect is investigated for a high fractional mass resolution spectrometry. A stochastic procedure like the Wiener or Brownian processes are potentially used in quadrupole ion traps (QIT). Issue examined are the sta- bility diagrams for noise coefficient, as well as ion trajectories in real time for noise coefficient, . The simulated results have been obtained with a high precision for the resolution of trapped ions. Furthermore, in the lower mass range, the impulse voltage including the stochastic potential can be considered quite suitable for the quadrupole ion trap with a higher mass resolution.